PreprintCC BY 4.0arXiv
Threshold-Free Symmetry-Enriched Topological Quantum Memory
Abstract
We show that non-Abelian symmetry enrichment can protect a toric code memory against incoherent electric noise at any bond error probability p∈[0,1]. For a toric code on the honeycomb lattice coupled to Sp(N) rotors, with electric anyons carrying the fundamental representation, we construct an efficient minimum-weight decoder whose logical error probability decays exponentially with system size for N≥40, a conservative sufficient bound. The same decoder also rules out strong-to-weak spontaneous symmetry breaking in the fundamental channel of Sp(N) under the corresponding local decoherence in two dimensions. The construction extends to other symmetries, including SU(N).
Related
- Topological Quantum Error-Correcting Thresholds of a Symmetry-Enriched Toric Code
- Symmetry-enriched topological order in tensor networks: Defects, gauging and anyon condensation
- Gauging Modulated Symmetries: Bond Algebras, Higher-Form Symmetries, and Symmetry-Enriched Topological Order
- Proof of a positive coherent-error threshold for topological quantum codes
- Symmetry-Enforced Topological Structures in Quantum Phase Diagrams
BibTeX
@misc{sarma2026thresholdfree,
title = {{Threshold-Free Symmetry-Enriched Topological Quantum Memory}},
author = {Abhijat Sarma and Ruochen Ma and Cenke Xu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07017},
eprint = {2611.07017},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07017},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Threshold-Free Symmetry-Enriched Topological Quantum Memory
AU - Abhijat Sarma
AU - Ruochen Ma
AU - Cenke Xu
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.07017
UR - https://arxiv.org/abs/2611.07017
AB - We show that non-Abelian symmetry enrichment can protect a toric code memory against incoherent electric noise at any bond error probability p∈[0,1]. For a toric code on the honeycomb lattice coupled to Sp(N) rotors, with electric anyons carrying the fundamental representation, we construct an efficient minimum-weight decoder whose logical error probability decays exponentially with system size for N≥40, a conservative sufficient bound. The same decoder also rules out strong-to-weak spontaneous symmetry breaking in the fundamental channel of Sp(N) under the corresponding local decoherence in two dimensions. The construction extends to other symmetries, including SU(N).
ER -